间歇结晶过程最佳操作时间表安排的研究

Optimal Scheduling for Batch Cooling Crystallization Processes

本研究对间歇冷却结晶过程的数学模型进行了分析,根据动态法测定得到的结晶成核速率B与成长速率G相关于降温速率U的函数关系的经验式,推导出描述过程的状态方程组,协状态方程组及Hamitonian函数,应用Pontryagin极大值原理对过程进行了最优控制条件的计算,建立了一个求解间歇冷却结晶最佳操作时间表安排的新型应用软件.并在DTB型工业规模的结晶器中进行了冷却间歇结晶实验.软件计算结果与实验结果的一致性,充分验证了软件的适用性.本研究所建立的简捷法策略与应用软件可用于指导Ⅱ类结晶物系间歇冷却结晶过程的操作与设计.

In this paper, the Pontryagin maximum principle is used to solve the mathematical mode) for batch processes of cooling crystallization. On the basis of the function relating the rate of nucleation B and the the rate of crystal growth G to the rate of cooling u as is measured by the batch method, the equation of state, Hamiltonian function, adjoint equations describing the processes are developed. An applied software is established to compute the conditions of optimized control. For the sake of verification of the method mentioned above, experiments with aqueous solutions of (NH4)2SO4 and NaNO2 were conducted in both MSMPR crystallizer of 4L and DTB crystallizer of 700L. The particles of 210 samples were sized by means of Coulter counter. Good agreement between computations and experimentations show that, this software can be applied to design and analysis of operations